In this paper we present a polynomial time algorithm for computing a Hausdorff core of a polygon with a single reflex vertex. A Hausdorff core of a polygon P is a convex polygon Q...
A watchman tour in a polygonal domain (for short, polygon) is a closed curve such that every point in the polygon is visible from at least one point of the tour. The problem of fin...
Let S be a set of points in the plane in general position. A triangulation of S will be called even if all the points of S have an even degree. We show how to construct a triangul...
Assume that two points p and q are given and a finite ordered set of simple polygons, all in the same plane; the basic version of a touring-a-sequence-of-polygons problem (TPP) is...
In this paper we devise a new geometric spanner based on a generalization of the known Stable Roommates algorithm. This spanner is on the "path" between the Yao graph an...
Given a set B of n blue points in general position, we say that a set of red points R blocks B if in the Delaunay triangulation of B R there is no edge connecting two blue points...
Oswin Aichholzer, Ruy Fabila Monroy, Thomas Hackl,...
We prove several new results concerning k-sets of point sets on the 2-sphere (equivalently, for signed point sets in the plane) and k-sets in 3-space. Specific results include sph...
A random polygon is the convex hull of uniformly distributed random points in a convex body K R2 . General upper bounds are established for the variance of the area of a random p...